Thermal Expansion

Almost everything grows when it warms up. Find how much a rail, beam or pipe expands — and how much force it pushes with if it is held so it cannot.

MaterialsThermal stressExpansion joints

Inputs

Input examples

α is the linear expansion coefficient in millionths per degree (10⁻⁶/K). Pick a material or type your own values.

Material

Expansion coefficient α (10⁻⁶ per °C)

Young’s modulus E — for the restrained stress

The part

Length L

Start temperature (°C)

End temperature (°C)

Cross-section — optional, for the force

Room to Move

Heat makes atoms vibrate more, so they take up a little more room. For most solids the length grows in proportion to the temperature rise, by a fraction α per degree — about 12 millionths for steel and concrete, twice that for aluminium.

That sounds tiny, but a 25 m steel rail grows 15 mm between a winter night and a summer day. If it cannot move, it pushes with a stress of E·α·ΔT — over 100 MPa — enough to buckle tracks. That is why bridges have expansion joints and old rails had gaps.

12×10⁻⁶steel and concrete

23×10⁻⁶aluminium

Invaralmost none

EαΔTstress if held

Length Change vs. Temperature

ΔL

your temperature range

Result

Enter the values above

Key Relations

Linear Expansion

Valid for moderate temperature changes, where α hardly changes.

Example:

Thermal Stress

If the part is held fully, the expansion it is denied becomes a compressive strain α·ΔT.

Example:

Volume

Every direction grows by the same fraction, so the volume grows three times as fast.

Sources & Verification

References

D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 18 (Temperature, Heat, and the First Law of Thermodynamics).
R. C. Hibbeler, Mechanics of Materials in SI Units, 10th ed., Pearson, 2018 — Ch. 4 (Axial Load).